Directions say that I have to solve and graph the equation using words.I have to include whether the lines are dotted or solid, how to graph each of them and where the solution is shaded.

2x-3y>_9 and -x-4y>_8

both should be solid, because the solution is greater than OR equal to the line.

which way should the shading be though?

solve for y in each equation, and it answers your question.

2x-3y>=9
y<=-3+2x/3 so the area BELOW y (y is less than or equal to the line..)
check my math

and
y<=-1/4 x -8 again, it says y is on or below the line...(less than or equal)

what.?

To solve and graph the given equations, follow these steps:

Equation 1: 2x - 3y ≥ 9

1. Solve for y:
Subtract 2x from both sides: -3y ≥ -2x + 9
Divide both sides by -3 (remember to reverse the inequality sign when dividing by a negative number): y ≤ (2/3)x - 3

2. Graphing:
- Draw a straight line with a slope of (2/3) passing through the point (-3, 0).
- Since the inequality is "y ≤," the shading should be below the line.
- The line should be solid because the inequality includes "or equal to."

Equation 2: -x - 4y ≥ 8

1. Solve for y:
Subtract -x from both sides: -4y ≥ x + 8
Divide both sides by -4 (remember to reverse the inequality sign when dividing by a negative number): y ≤ (-1/4)x - 2

2. Graphing:
- Draw a straight line with a slope of -1/4 passing through the point (-2, 0).
- Since the inequality is "y ≤," the shading should be below the line.
- The line should be solid because the inequality includes "or equal to."

To determine where the solution is shaded, you need to look at the overlapping region. Since both inequalities have "y ≤," the shaded area will be below both lines. The shaded region will be the portion of the graph that exists below both lines of the inequalities.